Subjects geometry, arithmetic, time calculations

Polygon Parallel Sides

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Polygon Parallel Sides


1. The problem asks for the number of pairs of parallel sides in each polygon. 2. From the given data: - Polygon 34 has 2 pairs of parallel sides. - Polygon 35 has 1 pair of parallel sides. - Polygon 36 has 4 pairs of parallel sides. - Polygon 37 has 0 pairs of parallel sides. 3. Next, petrol costs are given for garages A, B, and C, and Carol needs to fill 20 litres. - Garage A: 137p per litre, so cost = $20 \times 137 = 2740$ pence = 27.40 pounds. - Garage B: 139p per litre, so cost = $20 \times 139 = 2780$ pence = 27.80 pounds. - Garage C: 138p per litre, so cost = $20 \times 138 = 2760$ pence = 27.60 pounds. 4. Carol has 27.50 pounds. - Garage A cost: 27.40 pounds (affordable) - Garage B cost: 27.80 pounds (not affordable) - Garage C cost: 27.60 pounds (not affordable) 5. Carol should go to garage A to fill up her car. 6. The most expensive garage is B at 27.80 pounds. - Additional money needed = $27.80 - 27.50 = 0.30$ pounds. 7. Watch gains 2 minutes every 24 hours. - From 10 a.m. to 10 p.m. same day is 12 hours, so watch gains $\frac{2}{24} \times 12 = 1$ minute. - At 10 p.m. same night, watch shows 10:01 p.m. 8. From 10 a.m. Monday to 10 a.m. Tuesday (24 hours), watch gains 2 minutes. - So at 10 a.m. Tuesday, watch shows 10:02 a.m. 9. From 10 a.m. Monday to 10 a.m. Wednesday (48 hours), watch gains $2 \times 2 = 4$ minutes. - So at 10 a.m. Wednesday, watch shows 10:04 a.m. 10. From 10 a.m. Monday to 10 a.m. next Monday (7 days = 168 hours), watch gains $\frac{2}{24} \times 168 = 14$ minutes. - So at 10 a.m. next Monday, watch shows 10:14 a.m. 11. Jasmina and Sharon shared 24 book tokens. - Jasmina had 2 more than Sharon. - Let Sharon have $x$ tokens, then Jasmina has $x + 2$. - Total: $x + (x + 2) = 24 \Rightarrow 2x + 2 = 24 \Rightarrow 2x = 22 \Rightarrow x = 11$. - Sharon has 11 tokens, Jasmina has 13 tokens. 12. Minutes between noon and 13:29: - 1 hour 29 minutes = $60 + 29 = 89$ minutes. 13. Weeks in 266 days: - $\frac{266}{7} = 38$ weeks (ignoring remainder). Final answers: - Polygon pairs: 34=2, 35=1, 36=4, 37=0 - Garage choice: A - Extra money needed: 0.30 - Watch times: 10:01 p.m. Monday, 10:02 a.m. Tuesday, 10:04 a.m. Wednesday, 10:14 a.m. next Monday - Tokens: Jasmina 13, Sharon 11 - Minutes: 89 - Weeks: 38